Past temperatures are important because they tell us how much natural variation exists in the climate. And the reason the last 7000 years are of particular interest is that the modern times happen to have the strongest solar activity (and therefore the weakest cosmic rays) for thousands of years. Cosmic rays create charged particles in the atmosphere and effect the formation of clouds. Clouds have huge effects on weather and climate. So if solar acitivity (also called space weather) effects earth's climate, the modern period should show this strongly. Here's a graph from a recent peer reviewed article on solar activity over the last 9000 years. The point is that the present is the time of the weakest cosmic ray intensity ever. So if there is any relation between cosmic ray intensity and climate, knowing the climate of the past, as well as the cosmic ray intensity of the past can help explain the climate of the present (and the climate of the future). I've annotated the graph to show how the present is at the lowest part of the graphs:
9,400 years of cosmic radiation and solar activity from ice cores and tree rings
Steinhilber, Abreu, Beer, Brunner, Christi, Fischer, Heikkila, Kubic, Mann, McCracken, Miller, Miyahara, Oerter and Wilhelms
Affiliations: Swiss Federal Institute of Aquatic Science, Laboratory of Ion Beam Physics, Swiss Federal Institute of Technology, Climate and Environmental Physics at University of Bern, Australian Nuclear Science and Technology Organization, Institute for Physical Science and Technology at University of Maryland, Alfred Wegener Institute for Polar and Marine Research, and Institute for Cosmic Ray Research at University of Tokyo
Proceedings of the National Academy of Sciences of the United States of America
April 17, 2012, Volume 109, Issue 6, 5967-5971.
Abstract: ... The newly derived records have the potential to improve our understanding of the solar dynamics and to quantify the solar influence on climate.
http://www.pnas.org/content/109/16/5967.full
This graph of solar activity (from the same link) shows that solar activity of the last 9000 years is similar to the climate over that period, as measured in a Chinese cave. Uh, note that the graph is shown upside down so that it matches ups and downs with the cosmic ray intensity graph shown above:
The above concept, (that the sun effects the climate, LOL) is being explored by geologists. Here are some more articles on the subject:
Persistent link between solar activity and Greenland climate during the Last Glacial Maximum
Adophi, Muscheler, Svensson, Aldahan, Possnert, Beer, Sjolte, Bjorck, Matthes and Theiblemont
Nature Geoscience 7, 662-666 (2014)
We conclude that the mechanism behind solar forcing of regional climate change may have been similar under both modern and Last Glacial Maximum climate conditions.
...
The Sun is the main energy source for the Earth’s climate system. Satellite observations indicate variations in total solar irradiance (TSI) of about 1 W m−2 associated with the solar 11 yr cycle
1. Despite these small changes in forcing
there is compelling evidence for a solar influence on climate arising from palaeoclimate studies (see ref.
1 and references therein). One proposed mechanism to amplify the Sun’s influence on climate involves the relatively large modulation of the solar ultraviolet output, which alters the radiative balance in the stratosphere through ozone feedback processes and eventually propagates downwards causing changes in the tropospheric circulation
1. Palaeoclimate studies allow an assessment of solar forcing of climate under various past orbital configurations and mean climate states, and thus may provide valuable insight into climate sensitivity to and mechanisms of solar forcing.
...
http://www.nature.com/ngeo/journal/v7/n9/full/ngeo2225.html
Late Holocene Sedimentary Response to Solar and Cosmic Ray Activity Influenced Climate Variability in the NE Pacific
Patterson, Prokoph and Chang, Sedimentary Geology, Volume 172, Issues 1-2, pages 67-84, November 2004.
Marine-laminated sediments along the NE Pacific coast (Effingham inlet, Vancouver Island) provide an archive of climate variability at annual to millennial scales. ...
...
6. Conclusions
Solar activity appears to have a major influence on regional and global climate as is recorded in the sedimentation patterns and diatom abundance data from Effingham Inlet, British Columbia.
http://www.sciencedirect.com/science/article/pii/S0037073804002507
http://www.essc.psu.edu/essc_web/seminars/spring2006/Mar1/Bond et al 2001.pdf
Persistent Solar Influence on North Atlantic Climate During the Holocene
Bond, Kromer, Beer, Muscheler, Evans, Showers, Hoffmann, Lotti-Bond, Hajdas and Bonani
Surface winds and surface hydrography in the subpolar North Atlantic appear to have been influenced by variations in solar output throughout the Holocene.
Science, December 7, 2001, 294, 5549
...
The results of this study demonstrate that Earth's climate system is highly sensitive to extremely weak perturbations in the Sun's energy output, not just on decadal scales that have been investigated previously, but also on centennial to millenial time scales documented here. ... Our findings support the presumption that solar variability will continue to influence climate in the future, which up to now has been based on extrapolation of evidence from the last 1000 years. ...
http://www.essc.psu.edu/essc_web/seminars/spring2006/Mar1/Bond et al 2001.pdf
Changes in solar activity and Holocene climate shifts derived from 14C wiggle-matched dated peat deposits
Mauquoy, Geel, Blaauw, Speranza and Pilcht
The Holocene, January 2004, Vol 14, No 1, 42-52
...
The 14C wiggle-matched peat sequences which form the subject of this review have served to precisely date palaeoclimatic change during the Bronze Age/Iron Age transition and the 'Little Ice Age'. They have revealed a correspondence between these changes in climate and changes in solar activity as recorded by variations in Delta 14C.
...
http://hol.sagepub.com/content/14/1/45.refs
The problem is that rising temperatures naturally increase the CO2 in the air because warm temperatures imply warm ocean water and warm water dissolves less CO2. So the historic graphs do not show causation, just correlation. The period of accurate temperature records, 1850 to 2000 corresponds to one of increasing temperatures and increasing CO2 so you cannot extract phase information from it. To get phase information you need to go through at least 180 degrees of a cycle and better to see a few full cycles. (Of course I ended the "period of accurate temperature records" at 2000 because you claim that the temperature records after that were inaccurate, LOL.)